Pith Number

pith:QSN7DNBK

pith:2015:QSN7DNBKB52V27P5H7ILQNYZKP

not attested not anchored not stored refs pending

The optimal Hardy--Littlewood constants for $2$-homogeneous polynomials on $\ell_{p}(\mathbb{R}^{2})$ for $2<p\leq4$ are $2^{2/p}$

D. Nunez-Alarcon, D. Pellegrino, W. Cavalcante

arxiv:1507.02984 v2 · 2015-07-10 · math.FA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QSN7DNBKB52V27P5H7ILQNYZKP}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T01:26:42.361325Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

849bf1b42a0f755d7dfd3fd0b8371953f4db0d0815484db015c951ce9bc06f6a

Aliases

arxiv: 1507.02984 · arxiv_version: 1507.02984v2 · doi: 10.48550/arxiv.1507.02984 · pith_short_12: QSN7DNBKB52V · pith_short_16: QSN7DNBKB52V27P5 · pith_short_8: QSN7DNBK

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/QSN7DNBKB52V27P5H7ILQNYZKP \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 849bf1b42a0f755d7dfd3fd0b8371953f4db0d0815484db015c951ce9bc06f6a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3742610660e01fbac58045dad11b8965290f6762933cb5e3681d7daa171a9474",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-07-10T18:41:15Z",
    "title_canon_sha256": "409745ba853b826d5c939e464fe6833da153f1fe64a914603d85a0cd74e40075"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.02984",
    "kind": "arxiv",
    "version": 2
  }
}